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A novel method of digital image encryption using graph theory

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Abstract

This paper proposes a new technique for image data security using the concepts from graph theory. The proposed technique considers the pixels of the digital image as vertices of a graph and defines edges between vertices with some real weight to each edge. Using the minimal spanning tree (MST) and weighted adjacency matrix of MST, the encryption and decryption algorithm for the color digital image are proposed. The experimental results and the security analysis of the proposed technique are given to validate the feasibility and robustness of the proposed method. Statistical analysis like histogram, correlation, and entropy confirm the robustness of the proposed method against statistical attacks. The experimental results also show that the proposed technique is resistant to brute force and occlusion attacks.

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References

  1. Acharya B, Rath GS, Patra SK, Panigrahy SK (2007) Novel method of generating self invertible matrix for hill cipher algorithm. Int J Security 1(1):14–21

    Google Scholar 

  2. Yu SS, Zhou NR, Gong LH, Nie Z (2020) Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system. Opt Lasers Eng 124:105816–105826. https://doi.org/10.1016/j.optlaseng.2019.105816

  3. Chen H, Liu Z, Tanougast C, Blondel W (2021) Comment on “A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation.’’. Opt Laser Technol 138:106901. https://doi.org/10.1016/j.optlastec.2020.106901

    Article  Google Scholar 

  4. Etaiwi WMA (2014) Encryption using graph theory. J Sci Res Rep 3(19):2519–2527

    Google Scholar 

  5. Farah MAB, Guesmi R, Kachouri A, Samet M (2020) A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation. Opt Laser Technol 121:105777. https://doi.org/10.1016/j.optlastec.2019.105777

    Article  Google Scholar 

  6. Faridnia S, Fae’z K (2010) Image encryption through using chaotic function and graph. Int Conf Comput Vision Graphics, Warsaw, Poland, pp 352–359

    Google Scholar 

  7. Goel N, Raman B, Gupta I (2014) Chaos based joint compression and encryption framework for end-to-end communication systems. Advances in Multimedia, Article ID 2014:14. https://doi.org/10.1155/2014/910106

    Article  Google Scholar 

  8. Guleria V, Mishra DC (2021) Multiple RGB image encryption algorithm with multilayers by Affine Hill Cipher with FrDCT and Arnold Transform. Fractals 29(6):2150151–1308

    Article  Google Scholar 

  9. Joshi AB, Kumar D, Gaffar A, Mishra DC (2020) Triple color image encryption based on 2D multiple parameter fractional discrete Fourier transform and 3D Arnold transform. Opt Lasers Eng 133:106139. https://doi.org/10.1016/j.optlaseng.2020.106139

    Article  Google Scholar 

  10. Joshi AB, Kumar D, Mishra DC, Guleria V (2020) Colour-image encryption based on 2D discrete wavelet transform and 3D logistic chaotic map. J Mod Opt 67(10):933–949. https://doi.org/10.1080/09500340.2020.1789233

    Article  MathSciNet  Google Scholar 

  11. Joshi AB, Kumar D, Mishra DC (2021) Security of Digital Images Based on 3D Arnold Cat Map and Elliptic Curve. Int J Image Graphics 21(1):2150006–21500026. https://doi.org/10.1142/S0219467821500066

    Article  Google Scholar 

  12. Liansheng S, Cong D, Xiao Z, Ailing T, Anand A (2019) Double-image encryption based on interference and logistic map under the framework of double random phase encoding. Opt Lasers Eng 122:113–122. https://doi.org/10.1016/j.optlaseng.2019.06.005

    Article  Google Scholar 

  13. Liao X, Yu Y, Li B, Li Z, Qin Z (2019) A new payload partition strategy in color image steganography. IEEE Trans Circuits Syst Video Technol 30(3):685–696

    Article  Google Scholar 

  14. Liao X, Yin J, Chen M, Qin Z (2020) Adaptive payload distribution in multiple images steganography based on image texture features. IEEE Trans Dependable Secure Comput 19(2):897–911

    Google Scholar 

  15. Liao X, Li K, Zhu X, Liu KJR (2020) Robust detection of image operator chain with two-stream convolutional neural network. IEEE J Sel Top Signal Process 14(5):955–968

    Article  Google Scholar 

  16. Tokareva N (2014) Connections between graph theory and cryptography. Graphs and Groups, Cycles and Coverings, Novosibirsk, Russia, pp. 23-26

  17. Priyadarsini PLK (2015) Survey on some applications of graph theory in cryptography. J Discret Math Sci Cryptogr 18(3):209–217. https://doi.org/10.1080/09720529.2013.878819

    Article  MathSciNet  Google Scholar 

  18. Rajput SK, Nishchal NK (2017) Optical double image security using random phase fractional Fourier domain encoding and phase-retrieval algorithm. Opt Commun 388:38–46. https://doi.org/10.1016/j.optcom.2016.11.002

    Article  Google Scholar 

  19. Rehman A, Liao X, Wang H (2021) An innovative technique for image encryption using tri-partite graph and chaotic maps. Multimed Tools Appl 80(14):21979–22005. https://doi.org/10.1007/s11042-021-10692-8

    Article  Google Scholar 

  20. Shafique A, Ahmed F (2020) Image encryption using dynamic S-box substitution in the wavelet domain. Wirel Pers Commun 115(3):2243–2268

    Article  Google Scholar 

  21. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423

    Article  MathSciNet  Google Scholar 

  22. Sun X, Shao Z, Shang Y, Liang M, Yang F (2021) Multiple-image encryption based on cascaded gyrator transforms and high-dimensional chaotic system. Multimed Tools Appl 80(10):15825–15848

    Article  Google Scholar 

  23. Taneja N, Raman B, Gupta I (2011) Selective image encryption in fractional wavelet domain. Int J Electron Commun 65(4):338–344

    Article  Google Scholar 

  24. Taneja N, Raman B, Gupta I (2011) Chaos based partial encryption of spiht compressed images. Int J Wavelets Multiresolut Inf Process 09(02):317–331

    Article  Google Scholar 

  25. Taneja N, Raman B, Gupta I (2012) Combinational domain encryption for still visual data. Multimed Tools Appl 59(3):775–793. https://doi.org/10.1007/s11042-011-0775-4

    Article  Google Scholar 

  26. Tokareva N (2014) Connections between graph theory and cryptography. Graphs and Groups, Cycles and Coverings, Novosibirsk, Russia, pp 23–26

    Google Scholar 

  27. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612. https://doi.org/10.1109/TIP.2003.819861

    Article  Google Scholar 

  28. Yamuna M, Karthika K (2015) Data transfer using bipartite graphs. Int J Advance Research Sci Eng 4(2):128–131

    Google Scholar 

  29. Yu SS, Zhou NR, Gong LH, Nie Z (2020) Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system. Opt Lasers Eng 124:105816–105826. https://doi.org/10.1016/j.optlaseng.2019.105816

    Article  Google Scholar 

  30. Zhang W, Wang S, Han W, Yu H, Zhu Z (2020) An image encryption algorithm based on random hamiltonian path. Entropy 22(1):73. https://doi.org/10.3390/e22010073

    Article  MathSciNet  Google Scholar 

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Acknowledgements

Authors are thankful to the anonymous reviewers for their valuable comments and suggestions that greatly improved the manuscript

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Authors and Affiliations

  1. Department of Mathematics and Astronomy, University of Lucknow, Lucknow, -226007, U.P, India

    Anand B. Joshi, Dhanesh Kumar & Sonali Singh

  2. Block-III, Old JNU Campus, New Delhi, -110067, India

    Sachin Kumar

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  1. Anand B. Joshi
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  2. Dhanesh Kumar
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  3. Sachin Kumar
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  4. Sonali Singh
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Correspondence to Anand B. Joshi.

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Second author is supported by Council of Scientific and Industrial Research (CSIR), New Delhi, Government of India, under Grant No. F. No. 09/107(0385)/2017-EMR-I.

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Joshi, A.B., Kumar, D., Kumar, S. et al. A novel method of digital image encryption using graph theory. Multimed Tools Appl 83, 6803–6828 (2024). https://doi.org/10.1007/s11042-023-15698-y

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  • DOI: https://doi.org/10.1007/s11042-023-15698-y

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